double alngam ( double xvalue, int *ifault );
double alnorm ( double x, bool upper );
void gamma_inc_values ( int *n_data, double *a, double *x, double *fx );
double gammad ( double x, double p, int *ifault );
double r8_abs ( double x );
double r8_min ( double x, double y );
void timestamp ( void );
double dgamma(double alpha);
double ddgamma(double alpha);
double dIG(double alpha, double x, int index);
double ddIG(double alpha, double x, int index);
